Ikrimah narrates from Ibn Abbas (may Allah be pleased with them both) that the Prophet (peace and blessings be upon him) said: "Make use of ithmid (kohl), for it sharpens the eyesight and makes the hair grow." He stated that the Messenger of Allah (peace and blessings be upon him) had a kohl container from which he (peace and blessings be upon him) applied kohl every night, three times in each eye.
This is the most authentic of what has been narrated about the Prophet (peace and blessings be upon him) applying kohl.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8257
Muhammad bin Ubaydullah bin Abi Rafi' (may Allah have mercy on him) narrates from his father, and he from his grandfather (may Allah be pleased with him), that the Prophet (peace and blessings be upon him) used to apply ithmid kohl while he (peace and blessings be upon him) was fasting.
Muhammad bin Ubaydullah bin Abi Rafi' is not strong.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8258
Sayyidah Aishah (may Allah be pleased with her) narrates that the Prophet (peace and blessings be upon him) would sometimes apply kohl while he (peace and blessings be upon him) was fasting.
Sa'id al-Zubaydi is one of the unknown (majhul) teachers of Baqiyyah, who narrates alone what is not corroborated. It has also been narrated marfu' from Anas bin Malik, with a very weak chain, that he saw no harm in it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8259
Abu al-Nu'man al-Ansari narrates: My father narrated this to me from my grandfather; and his grandfather came to the Prophet (peace and blessings be upon him) and brought him to the Prophet (peace and blessings be upon him), and he (peace and blessings be upon him) passed his hand over his head and said: "Do not apply kohl during the day while you are fasting; apply ithmid kohl at night, for it sharpens the eyesight and makes the hair grow."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8260